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General procedure
Highly activated tantalum specimens with a total dose rate of more than 10 mSv/h from an irradiation program for materials science at PSI 47 , were used as the source of 146 Sm .Using radiochemical separation and purification methods, namely a sequence of five consecutive ion chromatographic separations with four different ion exchange resins 48 , a samarium fraction containing ppb amounts of 146 Sm in nitric acid medium (hereafter referred to as the "Sm master-solution") was obtained by processing several of these tantalum samples.The performance of the chromatographic separations was monitored with different radiolanthanides, which ensure an accurate localization of the elution fraction containing only samarium.To accurately monitor the samarium concentration during the separation procedures, and all subsequent treatments, 145 Sm was added to the samarium solution as an internal γ-ray emitting radiotracer.The applied method generally guarantees baseline separated chromatograms of the lanthanides, showing a suppression of the neighboring elements by a factor of 100 at least.In particular, it was shown in 48 that the neodymium impurity in the samarium fraction, which contributes to the 146-mass isobar, could be suppressed by at least a factor of 1000 with respect to 146 Sm.
After the Sm master-solution was prepared, gravimetrically quantified aliquots were taken for the determination of the 146 Sm concentration by multicollector inductively coupled plasma mass-spectrometry (MC-ICP-MS) without any further chemical treatment.The reverse isotope dilution mass-spectrometry 49 (IDMS) and the internal standard method coupled with a gravimetric standard addition method (ISM-SAM) 50 were applied.Additionally, a 146 Sm sample for α-spectrometric measurement was prepared.For this purpose, another gravi- metrically determined aliquot of the Sm master-solution was taken and used for the deposition of a thin and uniform layer using the molecular plating (MP) technique (also referred to as "electrodeposition") 51 .The solution used for MP is referred to in the following as the "Sm plating-solution".Graphite was chosen as the deposition substrate due to its general chemical inertness.
The deposition yield of samarium was determined by monitoring the activity of the added 145 Sm radiotracer in the aliquot of the Sm master-solution before deposition and subsequently in the deposited layer on the graphite foil.Both γ-spectrometric measurements were performed in matching geometric configurations using the same methodology and setup as described in 46 .After the MP procedure, the 146 Sm activity was quantified by α-spectrometry.The α-measurement was performed for 58 d at a defined solid angle.The absolute activity of the α-source was deduced by directly comparing the count rate measured for 146 Sm against the count rate of an 241 Am standard reference source with a certified activity.To minimize any geometric differences between the α-spectrometric measurements of 146 Sm and 241 Am , the area of deposited activities of both α-sources had the same diameter.In addition, custom-made sample holders were used for both α-measurements to ensure an identical distance between the sample surface and the detector.
The isotopic composition and concentration of the Sm plating-solution after MP was determined using an independent and complementary method, the thermal ionization mass spectrometry (TIMS).The sample for TIMS (hereafter referred to as "Sm TIMS-solution") was prepared by collecting the remaining Sm platingsolution and converting it to a nitric acid form.This additional mass spectrometry step acts as an independent confirmation of the number of 146 Sm atoms in the Sm master-solution.Furthermore, if the isotope ratios of samarium remain the same in both the Sm master-solution and the Sm TIMS-solution, it can be confirmed that no significant amount of samarium was added from external sources while the MP treatment.However, due to the chemical treatments performed during the preparation of the Sm plating-solution, the 146 Sm concentrations of the Sm master-solution (obtained by MC-ICP-MS) and the Sm TIMS-solution (measured by TIMS) will be different.Regardless, the results of the MC-ICP-MS and TIMS measurements can be interrelated by comparing the specific activity of 145 Sm in both solutions.For this purpose, a γ-spectrometric measurement also of the Sm TIMS-solution was performed.
The experimental steps for the re-determination of the half-life of 146 Sm are shown schematically in Fig. 1.Details of each technique used can be found in the section "Materials and methods", with further experimental details provided in the Appendix with Supplementary information ("SI Appendix"). (1) Unless otherwise noted, all uncertainties reported here were calculated according to the recommendations of the Guide to the expression of Uncertainty in Measurement (GUM) 52 and are given as combined standard uncertainties with a coverage factor k = 1 .

Results
The aim of the α-spectrometric measurements was to accurately determine the specific 146 Sm activity in the Sm master-solution, whereas the γ-spectrometric measurements of the radiotracer 145 Sm ( t 1/2 = 340(3) d , E γ = 61.2keV 53 ) were performed to ensure the quantitative traceability of all aliquots prepared from the Sm master-solution.The γ-measurement of the aliquot of the Sm master-solution ( γ-measurement_A) before MP, which was later used as Sm plating-solution, showed a count rate of 8.526(50) cps for 145 Sm on June 24, 2021.The selected experimental parameters, namely the organic solvent, applied voltage, current, and duration of MP, were intentionally chosen to minimize the thickness of the 146 Sm layer to avoid irregular film formation or detachment of the samarium layer from the deposition substrate due to hydrogen production.At the same time, a suitable count rate for the activity measurements and an excellent α-spectroscopic resolution must be guaran- teed.Systematic pre-experiments have shown that a significant increase in deposition yield can only be achieved at the expense of the quality of the α-sample.For this reason, a low deposition yield was accepted to ensure the best possible measurement result.The deposition layer obtained for α-spectrometry clearly show second-order interference colors (see Fig. 1) indicating a layer thickness below 500 nm.After the MP procedure, the γ-activity of the 145 Sm radiotracer deposited on the graphite foil ( γ-measurement_B) was determined on August 11, 2021 with 0.12462 (54) cps.Taking into account the radioactive decay of the radiotracer 145 Sm between the two γ-spectrometric measurements (i.e., 48 d), the samarium deposition yield of 1.684(27)% was derived.The latter includes an additional correction factor (for details see 46 ), which allows a more accurate comparison between the activity of 145 Sm contained in a solid deposited layer and in a liquid medium.The uncertainty in the half-life of 145 Sm was taken into account and included in the total uncertainty budget.
Since isotopes of the same element behave chemically identical, it is not possible to remove 147 Sm from the Sm master-solution by chemical means.However, the contribution of the 147 Sm α-decay to the 146 Sm α-peak was found to be only 0.148(32) mBq or 0.99(21)%.Although 148 Gd was largely chemically separated, trace amounts were still detectable in the α-spectrum due to its relatively short half-life of only 86.9(39) a 45 .From the α-spectrum, an activity of 15.97 (34) mBq was derived for 148 Gd in the plated sample, which corresponds to a concen- tration of ≈ 10 −15 mol/g 148 Gd (or 6 •10 8 at/g) in the Sm master-solution.This value is significantly below the detection limit of all mass spectrometric methods used in this work.The specific 146 Sm activity 0.1416(37) Bq/g of the Sm master-solution was determined taking into account the used 6.293167 (20) g of this solution and the derived samarium deposition yield of 1.684( 27)%.
The concentration of 146 Sm in the Sm master-solution was determined using both MC-ICP-MS and TIMS.For MC-ICP-MS, the isotope ratio 147 Sm/ 146 Sm of 9.061 (11) was deduced from measurements where no samarium reference standards were added.The concentration of 146 Sm in the Sm master-solution was determined to be 0.9748(98) nmol/g using ISM-SAM and 0.9900(54) nmol/g using the IDMS technique.The averaged value of 0.982 (15) nmol/g was used as the MC-ICP-MS result for further calculations (Table 1).
The concentration of 146 Sm in the Sm master-solution was also measured using TIMS.The isotope ratio 147 Sm/ 146 Sm was determined to be 9.0618(93) by using five loads with different amounts of the Sm TIMS- solution, and the 146 Sm concentration was quantified using the IDMS technique to be 0.36378 (36) nmol/g.As mentioned above, this value differs significantly from the concentration of 146 Sm in the Sm master-solution due to the chemical treatments during MP.However, the perfect agreement of the 147 Sm/ 146 Sm isotope ratio obtained by TIMS and MC-ICP-MS proves that no significant amounts of natural samarium were introduced from external sources during MP and the preparation of the Sm TIMS-solution.Therefore, it was possible to establish an interrelation between the 146 Sm concentration in the Sm TIMS-solution and in the Sm master-solution by comparing their 145 Sm γ-activities evaluated at the same reference date and account for the concentration change in the Sm TIMS-solution.From the results of γ-measurement_C, a specific 145 Sm count rate in the Sm TIMS-solution of 0.29936 (31) cps/g was determined on March 3, 2022.The specific count rate of 145 Sm in the Sm master-solution was calculated for this date from γ-measurement_A to be 0.8104(59) cps/g.Considering the TIMS result, the concentration of 146 Sm in the Sm master-solution is 0.9848(73) nmol/g, which is in excellent agreement with the Table 1.Results of the α-activity and mass-spectrometric measurements to determine the specific activity A (given in Bq/g), the 146 Sm concentration (given in nmol/g), and the number of atoms N per g of Sm master- solution.In Fig. 3, the result obtained here is shown alongside all other experimental half-life determinations (with the exception of the retracted value from Kinoshita et al. 27 ) and some selected theoretical half-life predictions of 146 Sm in relation of the date of the respective publication.A detailed assessment of all previous measurements discussing possible short comings is given in 40 .The theoretical publications [28][29][30][31][32][33][34][35][36][37][38] are restricted to half-life predictions not exceeding 150 Ma.Also, the attempt by Fang et al. 39 to combine the age determination of various Table 2. Uncertainty budget for the determination of the half-life of 146 Sm .Combined standard uncertainties with a coverage factor k = 1 are given.The partial uncertainty contributions of the half-lives of 133 Ba and 241 Am with 203 ppm and 10.5 ppm, respectively, as well as the contributions resulting from the weighing of 3.2 ppm are not shown in the table.open violet pentagon) from dating evaluation of different samples, some theoretical predictions [28][29][30][31][32][33][34][35][36][37][38] (open orange stars), and the individual results of Friedman et al. 25 presented as open gray diamonds in addition to the average value given in the paper.The value given by Dunlavey and Seaborg 58 was reported without any uncertainty and is, therefore, displayed as open circle.

Parameter
samples using different isotope chronometers and thereby perform a best-fit of the 146 Sm half-life could not sufficiently constrain this value to be suitable for a dating application.For a reliable application of the 146 Sm-142 Nd isotope chronometer, an accurate determination of the 146 Sm half-life is an essential prerequisite.With the recent retraction of the Kinoshita value 42 and the value determined here, the main problem has been addressed, leading to a significant improvement in the consistency of the data set.All previous half-life determinations were lacking in-depth documentation of the individual experimental steps, so that it is not possible to adequately consider possible systematic biases, as explained in detail in 40 .The present study contains an as complete as possible documentation of all experimental steps performed (see SI Appendix) and thus enables the assessment of possible artifacts.Based on this information, the half-life of 146 Sm was determined to be 92.0Ma with an uncertainty of less than 3%.
Additional independent determinations of the 146 Sm half-life using alternative methods, such as the ongoing studies with metallic magnetic calorimeters or transition edge sensors 56,57 , will complement these findings and help to establish a precise and accurate half-life value for this important chronometer.

Materials and methods
In total, an amount of 6.732910(20) g of Sm master-solution was obtained from the chemical treatment (for more details see description of "Method B" in 48 ) of the activated tantalum specimens (see SI Appendix Table SI 1).

Molecular plating
In preparation for the MP procedure, the custom-made plating cell consisting of polytetrafluoroethylene (described in 46,61 ) was cleaned by stepwise rinsing with 1 M HNO 3 , 18.2 M cm milliQ-water and isopropanol.A platinum wire spiral was used as anode and likewise cleaned.The cathode, a block of copper, was cleaned with 0.1 M citric acid, washed with MilliQ water and rinsed with isopropanol.The graphite deposition foil (thickness: 75 µ m, diameter of the deposition area: 20 mm, purity: 99.8%, Flexible Graphite, GoodFellow Cambridge Ltd.) was rinsed in isopropanol before MP.
For the MP procedure, a gravimetrically determined aliquot of 6.293167(20) g of the Sm master-solution (see SI Appendix Table SI 7) was filled into a custom-made polyether ether ketone vial (PEEK-vial).Before the MP procedure, the activity of the aliquot contained in the PEEK-vial was determined by a γ-spectrometric measurement ( γ-measurement_A).
After the γ-measurement, the samarium solution contained in the PEEK-vial was reduced to dryness at 70 • C under a N 2 gas flow to remove any residual HNO 3 and water.This was a necessary step to prevent the development of H 2 at the cathode, which generally affects the quality of the deposited layer 62 .Subsequently, the obtained residue was dissolved in 15 mL methanol.Due to the polar and protic nature of methanol and its ability to dissolve lanthanide nitrates similar like water, this organic compound was chosen as both the dissolution and plating medium.The Sm plating-solution was added into the plating cell, where a thin samarium layer with a diameter of 20 mm was molecular plated onto the graphite foil by applying a constant voltage of 30 V for 30 min.During the plating process, the distance between the two electrodes was approximately 10 mm.To avoid inhomogeneities in the deposition layer due to temperature fluctuations during deposition, the cathode was equipped with a Peltier cooler that kept the graphite foil at a constant temperature of 15 • C.

γ-Spectrometric measurements
All γ-spectrometric measurements of the 145 Sm radiotracer were performed with a Broad Energy Germanium (BEGe) γ-detector (Mirion Tech.-Canberra; crystal dimensions diameter: 61 mm, thickness: 25 mm).Data acquisition and analysis was performed using Genie 2000 Gamma Acquisition & Analysis software (Mirion Tech.-Canberra).Energy calibration was done using a certified point-like 152 Eu source (Physikalisch-Technische Bundesanstalt -"PTB").The full width at half maximum (FWHM) energy resolution was 0.57 keV at 61.25 keV.A dedicated sample holder was used to ensure the γ-spectrometric measurements in two geometrically equivalent positions as described in 46 (see SI Appendix Fig. SI 1).

γ-Measurement_A
The aliquot of the Sm master-solution taken for MP was filled into the custom-made PEEK-vial (inner diameter: 20 mm, thickness at the bottom: 1.0 mm) and evaporated to dryness at 70 • C under N 2 gas flow.The residue was dissolved with 400 µ L of 1 M HNO 3 .The PEEK-vial was placed on the lower stage of the sample holder in the Configuration_A (see SI Appendix Fig. SI 1).Additionally, a graphite deposition foil identical to the one used for MP was inserted between the bottom of the PEEK-vial and the detector endcap.The γ-spectrometric measurement of the 145 Sm contained in the PEEK-vial was performed for 3585 s live-time, i.e., the dead time corrected counting period (see SI Appendix Fig. SI 2 and, Table SI 8).The samarium solution in the PEEK-vial was then used for MP.

γ-Measurement_B
The 145 Sm activity contained in the deposition layer after MP was measured by placing the foil in Configuration_B of the custom-made sample holder (see SI Appendix Fig. SI 1).A PEEK-disk (thickness: 1.0 mm, identical to the bottom of the PEEK-vial) was placed on the bottom stage of the sample holder between the graphite foil and the detector endcap.The γ-spectrometric measurement was performed for 601015 s live-time (see SI Appendix

α-Spectrometric measurements
The Alpha-Analyst (Mirion Tech.-Canberra), an integrated α-spectrometer equipped with a passivated implanted planar silicon (PIPS) detector (Model A-450-21AM Mirion Tech.-Canberra; sensitive surface: 450 mm 2 ; energy resolution FWHM: 21 keV), was used for the activity quantification of the pure α-emitter 146 Sm .The data acquisition was performed with the Genie 2000 Alpha-Analysis software (Mirion Tech.-Can- berra).The energy calibration of the detector was performed with different α-sources: a point-like mixed source of 148 Gd and 244 Cm and a certified point-like three-line source with 239 Pu , 241 Am , and 244 Cm (Amersham International plc).The efficiency calibration of the detector was performed with a certified 241 Am reference standard (PTB, calibration reference no.PTB-6.11-2016-1769,A = 539(11) Bq as of 01.11.2016 00:00:00 CET, k = 2 ), which had the same 20 mm diameter as the samarium deposition on the graphite foil ( see SI Appendix Fig. SI 4).Geometrical differences between the 241 Am standard source and the deposited samarium sample were further minimized by custom-made sample holders to ensure that the measurements were performed at the same distance of 10.4 mm between the sample surface and the passivated entrance window of the PIPS detector.The shape of the individual α-peaks was parameterized according to a suggestion by Pommé and Marroyo 63 (see SI Appendix Tables SI 10, 11, and 12).

MC-ICP-MS
All measurements were performed with the Nu Instruments Plasma 3 MC-ICP-MS at PSI.For the masses of 143, 145 to 155, 157, 158, and 161, the ion beams were collected simultaneously in Faraday cups connected to amplifier systems with a 10 11 resistor in their feedback loop. 146Sm , which formed the weakest samarium ion beam, delivered a current between 0.3 pA and 0.6 pA over the entire three days of analysis.All analytes were introduced as solutions in 0.28 M HNO 3 using an Elemental Scientific APEX HF nebulizing system and a selfaspirating Elemental Scientific PFA-ST Microflow nebulizer consuming ca.50 µL/min.The operating power of the plasma was 1350 W. The analytes were measured 9 times at a low mass resolution.Each analysis consisted of 60 signal integrations, each 7.5 s long.Mixtures with different mass fractions of a reference samarium standard solution VHG-PSMN-100 (1000 µg/mL natural samarium in 5% HNO 3 , LOT: 1018557-8 from LGC Limited with a certified content of 0.9990(20) mg/mL; hereinafter referred to as "Sm LGC-standard") and a gadolinium reference standard solution Specpure (1000 mg/mL natural gadolinium in 5% HNO 3 , LOT: 223965 from Thermo Scientific Chemicals with a certified content of 0.9900(150) mg/mL; hereinafter referred to as "Gd Specpure-standard") with or without the addition of aliquots of the Sm master-solution was prepared and analyzed (see SI Appendix Tables SI 2, SI 3, and SI 4).The Gd-Sm solutions without Sm master-solution were used to characterize the relation between the extent of mass fractionation of gadolinium (interference-free 157 Gd/ 155 Gd ) and samarium (interference-free 147 Sm/ 149 Sm).
The mass fractionation was corrected applying the exponential mass fractionation law 64 by adding Gd Specpure-standard to the 146 Sm containing solutions.Mixed solutions of Sm LGC-standard and Gd Specpure- standard without aliquots of the Sm master-solution that were analyzed alongside the 146 Sm containing analytes served to characterized the relation between the magnitude of mass fractionation of gadolinium (interference-free 157 Gd/ 155 Gd ) and samarium (interference-free 147 Sm/ 149 Sm ).Assuming natural isotopy, the isobaric-interfer- ence-free gadolinium and samarium isotope ratios 157 Gd/ 155 Gd = 1.0566 (12)  65 and 147 Sm/ 149 Sm = 0.9213(12) 66 were used to characterize the mass fractionation magnitude.Thus, all signals of 146 Sm containing analytes were corrected for mass fractionation.From this procedure, an isotope ratio 147 Sm/ 146 Sm of 9.061 (11) was obtained.
A priori, there is no information about the isotopic abundances of neodymium in the 146 Sm containing ana- lytes.A natural isotope abundance cannot be presumed due to the artificial production of neodymium isotopes by the activation of tantalum specimens.Thus, interference corrections could only be performed if the isotopy of neodymium is close to natural samples.Monitoring the signals at masses 143 and 145, which represent isobaricinterference-free neodymium isotopes, provides the possibility to evaluate the isotope ratios 143 Nd/ 146 Sm and 145 Nd/ 146 Sm (see SI Appendix Table SI 13) and thus assess the isotope ratio 143 Nd/ 145 Nd .Note that this evaluation was only possible for the two analytes with the highest 146 Sm concentration, as the signals of 143 Nd and 145 Nd were generally close to and often below the quantification limit.This is a consequence of the chemical separation process, which guarantees a quantitative separation of neodymium and leads to a residual concentration that is at least 100 times lower than that of 146 Sm .This has also been confirmed by independent measurements (see 48 ).Consequently, only individual measurement runs in which the signals of both neodymium isotopes significantly exceeded the background values of 2 µ V were used, resulting in an isotope ratio 143 Nd/ 145 Nd of 1. 36(98).This value is consistent with the isotope ratio 143 Nd/ 145 Nd of natural sample 1.4682 (14) (calculated from 67 ).The interference corrections was therefore performed based on the 145 Nd signals assuming a natural isotopy of neodymium.Given the very low 145 Nd ion beam current in the sub-fA ranges, the calculated average contribution of neodymium to masses 146, 148, and 150 are 0.04% to 0.14%, 0.01% to 0.05%, and 0.01% to 0.05%, respectively.Thus, the inherent inaccuracies are estimated to be ≈ 0.035% at worst.Assuming natural neodymium abundances in the 146 Sm analytes to correct for interference is considered more accurate than not correcting for neodymium interference.The contribution of interfering 158 Dy to the overall signal at mass 158 was, at most ≈ 0.0002% and thus negligible.For this reason, no correction was made for isobaric interference due to 158 Dy.
All reported uncertainties for the 146 Sm concentrations include the 0.2% uncertainty of the Sm LGC-stand- ard.The uncertainty of both the IDMS method and the standard addition method is based on a Monte Carlo uncertainty propagation procedure that takes into account both weighing uncertainties and all measurement uncertainties of the respective inter-and intra-element isotope ratios.The reported average concentrations per method and their respective uncertainties cover the full range of possible results using all measurement data reported in SI Appendix Table SI 13.The uncertainty of the average of both methods includes the scatter 0.12% and the uncertainty propagation based on the uncertainties of the individual average values, about 1.0% and 0.55%, respectively (see SI Appendix Sect.SI 5).For all gravimetric steps, a yearly certified Mettler-Toledo XP56 balance (1 µ g scale interval) was used in a temperature-controlled room at 20 • C to 23 • C.

TIMS
After the MP procedure, the remainder of the Sm plating-solution was collected and the methanol evaporated at room temperature under N 2 gas flow.The remaining residue was treated with a mixture of 11 M HNO 3 and 30% H 2 O 2 (w/w in H 2 O) to ensure the decomposition of any traces of organic solvent.The liquid was then evaporated at 70 • C under N 2 gas flow and the remaining dissolved in 1 M HNO 3 .
The resulting Sm TIMS-solution was analyzed by TIMS without further purification.An aliquot of 0.51824(10) g was diluted with 0.5 M HNO 3 to a total weight of 102.84038(9) g in a 125 mL Teflon-FEP bottle.The isotopic composition and concentration of the Sm TIMS-solution were determined by TIMS on a modified MAT 261 at the Research School of Earth Sciences, The Australian National University.
The aim of these measurements was to determine the concentration of 146 Sm as precisely and accurately as possible.Thus, an established protocol for precise samarium and neodymium analysis from double filament loads (e.g., 68 ) was used.Sample solutions were evaporated with 20 µ L of 0.007 M H 3 PO 4 , loaded in 1.0 µ L of 0.5 M HNO 3 on outgassed rhenium filaments of a double filament (Re+Re) assembly, and analyzed using an established protocol for precise samarium and neodymium analysis from double filament loads (e.g., 68 ).The current of the ionization filament was set at 4.0 A and the current of the evaporation filament was varied between 0.8 A and 2.4 A. This allowed for the evaporation filament to achieve a stable ion beam at the maximum possible intensity lasting at least 2 h to 3 h.Since the Sm TIMS-solution has no known isotopic ratios that can be used for internal bias correction, the instrumental bias was corrected using the total evaporation and the incipient emission approaches that were discussed in detail by Amelin and Merle 69 .Two types of isotopic analyses after the TIMS measurements were performed, namely total evaporation (TE-TIMS) and incipient emission (IE-TIMS).For the measurements, a 6 Faraday cup configuration was used, where the samarium isotopes 146, 147, 149, and 152 were acquired, and possible neodymium interference was monitored on the masses 143 and 145.
Mainly the following measurements were performed.The original Sm TIMS-solution was used for a few measurements (5 loads) to determine the isotope ratio 147 Sm/ 146 Sm .A natural samarium solution prepared from high purity samarium metal (purity of metal 99.996% from Ames Laboratory; hereafter referred to as "Sm Amessolution") was used as primary concentration standard and as supporting isotopic standard (6 loads).In addition, the synthetic samarium isotope mixture GBW04605 (from the series of eleven Certified Reference Materials "Samarium Isotopic Reference Material in Nitric Acid Solution, GBW04601-GBW04611" of the National Institute of Metrology of P.R.China of the National Institute of Metrology of P.R. China; hereafter referred to as "Sm GBW-solution") was used as the primary isotope standard (5 loads).Mixtures of Sm TIMS-solution and Sm Ames-solution (6 analyzed mixtures, each 8 loads) were used for IDMS analysis (see SI Appendix Table SI  5).The size of the individual filament loads was between 1 ng and 100 ng samarium.The comparison between the bias correction with TE-TIMS and IE-TIMS showed a clear advantage of the TE-TIMS approach, which is consistent with the results of 69 for the analysis of potassium by surface ionization with double filaments.The mass bias correction for the TIMS measurements was performed using the power-law approach (see 70 and 71 ).The TE-TIMS analyses of the Sm-Ames solution and the Sm-GBW solution using the isotope ratios 149 Sm/ 147 Sm and 152 Sm/ 147 Sm gave a bias coefficient of 0. 99932(39) (0.074%), while IE-TIMS from the same runs showed a value of 1.0072(73) (0.28%).The IE-TIMS values scatter more, leading to a higher uncertainty of the bias coefficient (see SI Appendix Fig. SI 5).Therefore, all mass bias corrections in this study, including the analyses of the IDMS mixtures, were carried out using the value obtained by TE-TIMS (see SI Appendix Table SI 14).This leads to an isotope ratio 147 Sm/ 146 Sm of 9.0618(93), in perfect agreement with the values 147 Sm/ 146 Sm of 9.061(11) meaured using MC-ICP-MS.
The calculated total uncertainty on the 146 Sm concentration includes: (1) the concentration uncertainty of Sm Ames-solution (0.01%); (2) the difference between the average concentrations calculated using the Sm mastersolution and the dilute Sm TIMS-solution (0.077%); (3) the reproducibility of concentration calculations from a dilution series of five mixtures using Sm TIMS-solution (0.17%); and (4) the reproducibility of TE-TIMS bias correction (0.037%).

Figure 1 .
Figure 1.Schematic flowchart of the experimental steps followed in this work for the determination of the halflife of 146 Sm via the "direct method".

Figure 2 .
Figure 2. (a) Measured α-spectrum (dark blue histogram) of the plated samarium on a graphite foil together with its 1 σ-confidence interval (light blue shaded area).The total counting time was 5 •10 6 s or 58 d.The histogram bin size is 5.713 keV.The peak-fitting model includes the 146 Sm peak (green dashed dotted line), the 148 Gd peak (red dashed dotted line) and the 147 Sm peak (purple dashed dotted line) which is superimposed with a low-energy electronic noise and a background component.The sum of all these components is shown as a dark green line.(b) Residuals of the peak fit (dark blue histogram) are consistent with the Poisson count statistics of the spectrum (1σ-uncertainty, light blue shaded area).

Figure 3 .
Figure 3. Experimental data (circles) and theoretical predictions (stars) for the 146 Sm half-life throughout the past decades.The half-live value measured here (green circle) is plotted in comparison to previous half-live determinations 25,26, 58-60 (circles with the last name of the first author).In addition are the value by Fang et al.39 (open violet pentagon) from dating evaluation of different samples, some theoretical predictions[28][29][30][31][32][33][34][35][36][37][38] (open orange stars), and the individual results of Friedman et al.25 presented as open gray diamonds in addition to the average value given in the paper.The value given by Dunlavey and Seaborg 58 was reported without any uncertainty and is, therefore, displayed as open circle.
Fig. SI 2 and, result of the MC-ICP-MS analyses.The concentration of 146 Sm in the Sm master-solution (see Table1) is determined as the mean value of the MC-ICP-MS and TIMS results, i.e. 0.9836(87) nmol/g.By applying the obtained values for the number of atoms N and the activity A to Equation 1, a half-life t 1/2 = 92.0(26)Ma of 146 Sm results with a combined standard uncertainty of 2.76%.The uncertainty budget for all used data is given in Table2.
Vol.:(0123456789) Scientific Reports | (2024) 14:17436 | https://doi.org/10.1038/s41598-024-64104-6www.nature.com/scientificreports/averaged TableSI 8).After finalizing the TIMS analysis, the remainder of the Sm TIMS-solution was transferred from the Teflon-FEP transport bottle into a PEEK-vial, identical as the one used for γ-measurement_A.The transferred mass was determined gravimetrically (see SI Appendix TableSI 6).The sample was dried at 70 • C under a N 2 gas flow and dissolved in 400 µ L of 1 M HNO 3 .The PEEK-vial was then placed in the upper stage of the sample holder in Configuration_A (see SI Appendix Fig. SI 1 and Fig. SI 3 TableSI 9).A graphite deposition foil, identical to that used for MP was inserted between the bottom of the PEEK-vial and the detector end-cap.The γ-spectrometric measurement of the 145 Sm contained in the PEEK-vial was carried out for 431254 s live-time (see SI Appendix Fig.SI 3 and, Table SI 9).